Mysql update rows dynamically based on column input

I have the following issue. I have a table called titles with the following structure:

id int(10),
name varchar(100),

At some point later we added a new column called modified_name. It is defined as the same as name except that it is lower case and has all of the spaces replaced with a -. We added this column and so we needed to now get the right modified name value into each record of that column. To do this we wrote a PHP script that handled that by loading in values from the database and processing them, but that is highly inefficient. Is it possible to write a single UPDATE query that would add the correct value to each record in the titles table. I can think of ways to do this with a stored procedure and a while loop there in, but I want to know if something more efficient is possible. It there any way to achieve something like the following:

UPDATE `titles` 
    SET 
`modified_name` = LOWER(REPLACE(SELECT `name` FROM `titles` WHERE id = PRESENT_VALUE), ' ', '-');

The goal being to SET the modified_title column of every record in the titles table to a unique value that results from that record's name column as followed:

# Before modification update query
name = "Hello Goodbye" 
modified_name = ""    

# After modification update
name = "Hello Goodbye" 
modified_name = "hello-goodbye"

Thank you for your help, any advice on how best to do this would be appreciated.